WASHINGTON - US Senate Republicans and Democrats clashed bitterly over President Donald Trump's Supreme Court pick, with no signs that a potentially damaging Thursday showdown will be averted.

The Senate began formal debate on Tuesday on judge Neil Gorsuch, as opposition Democrats insisted they have the necessary votes to block his nomination through use of a tactic known as a filibuster.

Sixty votes are needed to overcome a filibuster and end debate in the 100-seat Senate. Republicans hold 52 seats.

Senate Majority Leader Mitch McConnell tweeted that "due to an unprecedented filibuster threat", he was setting up the crucial test vote for Thursday morning.

A confirmation vote follows on Friday, after which Congress shutters for a two-week recess.

The expected failure of the test vote sets the stage for Republican leaders to employ the "nuclear option", which would change Senate rules in order to advance the nomination - and all subsequent Supreme Court nominees - by a simple majority vote.

McConnell warned that the Democrats' filibuster could do something "truly detrimental to this body and to our country". Democrats were "hurtling toward the abyss, and trying to take the Senate with them. They need to reconsider", he said.

To overcome the filibuster, Republicans need eight Democrats to back Gorsuch, named by Trump to fill the seat of Antonin Scalia who died in February 2016.

To date, just four Democrats have announced their support. "They're pretty much dug in," Republican Senator John Thune said of Democratic colleagues.

McConnell will need to put the rules change to a majority vote. He said he has enough votes from his party for the change to succeed, but some Republicans have bristled at the nuclear option and how the threat of using it has poisoned the atmosphere.